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Robust \(T\)-optimal discriminating designs. (English) Zbl 1277.62188

Summary: This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the \(T\)-optimality criterion introduced by A.C. Atkinson and V.V. Fedorov [Biometrika 6, 57–70 (1975; Zbl 0308.62071)]. \(T\)-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and a standardized maximin approach to construct robust and efficient discriminating designs on the basis of the \(T\)-optimality criterion. It is shown that the corresponding Bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria. For the problem of discriminating between two polynomial regression models which differ in the degree by two the robust \(T-\)optimal discriminating designs can be found explicitly. The results are illustrated in several examples.

MSC:

62K05 Optimal statistical designs
62K25 Robust parameter designs
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 0308.62071
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References:

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